How can I import an addon into a Blender script?
There are addon utilities available in 2.77/scripts/modules/addon_utils.py which you can import into your script.

Here is an overkill example, lists all addons and then tries to enable addons named ['mesh_looptools','mocap_madness','goose']

import bpy
from addon_utils import check, paths, enable

def get_all_addons(display=False):
    """
    Prints the addon state based on the user preferences.
    """
    import sys
    paths_list = paths()
    addon_list = []
    for path in paths_list:
        bpy.utils._sys_path_ensure(path)
        for mod_name, mod_path in bpy.path.module_names(path):
            is_enabled, is_loaded = check(mod_name)
            addon_list.append(mod_name)
            if display:  #for example
                print("%s default:%s loaded:%s " % (mod_name, is_enabled, is_loaded))                
    return(addon_list)
#print all the addons and show if enabled and default
addons = get_all_addons(True)
#enable dependencies
addon_dependencies = ['mesh_looptools','MocapMadness','goose']
for addon in addon_dependencies:
    if addon in addons:
        is_enabled, is_loaded = check(addon)
        if not is_enabled:
            print("%s enabled" % addon)
            enable(addon)
    else:
        print("Error Dependency %s missing" % addon)


Answer from https://blenderartists.org/forum/showthread.php?234219-Check-if-Add-On-is-enabled-using-Python&amp;p=1970462&amp;viewfull=1#post1970462

Mainly only need

    is_enabled, is_loaded = check(addon)
    if not is_enabled:
        print("%s enabled" % addon)
        enable(addon)